Saturday, March 28, 2009

Catching another z

Been there, done that

On the one hand, my students never fail to surprise me. On the other, they can't help replaying the evergreen mistakes of the past. They have certain recurring problems.

Penmanship.

Yes, I know it may be on the verge of becoming a lost art, but in most math classes you still need to write stuff. By hand. We don't (yet) allow you to submit your answers by texting. You have to write stuff on paper. If you can't read your own writing, you are in big trouble. Each semester I inveigh against sloppy writing practices that permit students to confuse their own symbols with each other. I have students who sometimes cannot tell the difference between their own 4's and 9's. Their own 3's and 8's. And, of course, their own z's and 2's.

It is that last problem that just manifested itself in a big way again. As before, it sabotaged a student as she was trying to solve an equation for the variable z. The results are similarly disastrous.


The problem involved a proportion containing an unknown. As you can see, the student briskly applied cross-multiplication, even indicating her calculation with swoopy arrows to mark the source of her factors. Unfortunately, the product of 2 and z magically morphed into 4. When she copied the proportion, she wrote 2 and z as indistinguishable (even to her) symbols.

Careless handwriting is hardly the entire story. Faced with a nonsensical equation stating that 40 equals 4, she promptly divided both sides by 4. She concluded that the answer had to be 10, which she promptly wrote in the answer blank. Funny. Why didn't she pick 1? Perhaps because in her experience 1 is so seldom the answer. The 10 just looks better.

Of course, “looking better” is an odd criterion for someone who can't even read her own writing.

11 comments:

Rhoadan said...

This is why I long ago picked up the habit of putting a crossbar on my "z"s, a little trick I picked up from my freshman calc prof.

BTW, the verification word is "appere." Obviously this is how one of PZ's crazier correspondents spells "appear."

Chris A said...

That is one reason I took up crossing my Zs and 7s, European style. Clarity is a good thing...

Chris A said...

Serves me right for spending time looking for an insertable crossed-z character :)

Theo Bromine said...

I've been crossing "Z"s (zeds) since highschool (in Canada), (and I cross my zeroes to distinguish them from "O"s but I gave up crossing "7"s in university (in the US), after a TA took off marks because he couldn't figure out my crossed "7" and guessed it was a "4".

Wouldn't crossing "z"s be a useful technique to teach your students? Or would it cause problems in some other way?

Zeno said...

If you visited my previous post on the subject, you'd see that I make a point of suggesting crossed z's (the "mustache version") to those who are liable to confuse it with their 2's. But people never seem to think that I'm talking to them.

Eamon Knight said...

Another Z, 7 and 0 crosser here (though in this context, I would have used a lower-case cursive z, which looks nothing like a 2). I think it was while I was an undergrad, and had to develop the ability to take notes at high speed, but still be able to read them later, that I developed disambiguating styles for several letters and symbols. It didn't hurt that I was also taking Drafting at the time, where we were taught standard forms for every letter and numeral, in both cases (my 4, for example, is too angular to ever be confused with a 9).

ods15 said...

For me, the worst is 6 and lowercase 'b'.. I don't think there is any other pair of letters I confuse more, and in that rare case I make sure I am extra careful...

Lsquared said...

For me, the worst is 6 and lowercase 'b'.

This is the reason why I dislike the new way of teaching printed letters. If you learned to make a lowercase b the way I did (rather than the preferred way of teaching now), you would never confuse it with a 6 (make the down line of the b first, then make the curved line by going up and around, not down and around).

Patrick said...

One of my profs this semester has a tendency to make his 'z's and '2's identical to each other.

This has been a problem one more than one occasion, because he teaches a class on complex variables.

Taz said...

Good thing your student didn't divide both sides by 2. Then you would have had to explain why she didn't get any credit for having the "right" answer.

(I also cross Z's and 0's, but not 7's.)

Anonymous said...

This simply goes beyong careful penmanship. I asked my 5th grade son to do the problem. He looked for a moment and said z is 20.

This is a case of forgetting what the problem was in the midst of a trivial problem best done in one's head to boot.

I would agree that in a "real" more complex problem poor penmanship might get one off track. But again it is about knowing what you are doing - when you get off track that should be painfully obvious, so go back and find your error. For example;
40/4 = 4/4 = 10 looking at this one must suspect that something went wrong. Go figure out what went wrong, what was the goal? (solve for z) what happened to z anyway?

I, personally, have poor penmanship. I have suffered to correct my errors as a result, but I never got a wrong answer as a result.